Page "Centripetal force" Paragraph 91

Polar unit vectors at two times t and t + dt for a particle with trajectory r ( t ); on the left the unit vectors u < sub > ρ </ sub > and u < sub > θ </ sub > at the two times are moved so their tails all meet, and are shown to trace an arc of a unit radius circle.

Their rotation in time dt is dθ, just the same angle as the rotation of the trajectory r ( t ).